DSNEP#

Dense Nonlinear Eigenvalue Problem.

Notes#

The problem is expressed as \(T(\lambda)x = 0\), where \(T(\lambda)\) is a parameter-dependent matrix written as \(T(\lambda) = \sum_i E_i f_i(\lambda)\). The eigenvalues \(\lambda\) are the arguments returned by DSSolve().

The coefficient matrices \(E_i\) are the extra matrices of the DS, and the scalar functions \(f_i\) are passed via DSNEPSetFN(). Optionally, a callback function to fill the \(E_i\) matrices can be set with DSNEPSetComputeMatrixFunction().

Used DS matrices#

  • DS_MAT_E0 to DS_MAT_E9 - coefficient matrices of the split form of \(T(\lambda)\)

  • DS_MAT_X - eigenvectors

  • DS_MAT_A - (workspace) \(T(\lambda)\) evaluated at a given \(\lambda\) (SLP only)

  • DS_MAT_B - (workspace) \(T'(\lambda)\) evaluated at a given \(\lambda\) (SLP only)

  • DS_MAT_Q - (workspace) left Hankel matrix (contour only)

  • DS_MAT_Z - (workspace) right Hankel matrix (contour only)

  • DS_MAT_U - (workspace) left singular vectors (contour only)

  • DS_MAT_V - (workspace) right singular vectors (contour only)

  • DS_MAT_W - (workspace) auxiliary matrix of size \(n\times n\)

Implemented methods#

  • 0 - Successive Linear Problems (SLP), computes just one eigenpair

  • 1 - Contour integral, computes all eigenvalues inside a region

See Also#

DS: Direct Solver (or Dense System), DSCreate(), DSSetType(), DSType, DSNEPSetFN(), DSNEPSetComputeMatrixFunction()

Level#

beginner

Location#

src/sys/classes/ds/impls/nep/dsnep.c

Index of all DS routines Table of Contents for all manual pages Index of all manual pages